The formation of a fold along an edge of a supple piece such as a textile piece, is generally effected by hand by the operator who folds the piece parallel to the edge over a width corresponding to the desired width of the fold and introduces it, with the fold thus formed, into the stitching station. The fold is more or less regular depending on the operator's skill. A particular difficulty arises when the fold must contain an elastic band, as is the case in tracksuit trousers: the profile that the operator must follow lies beneath the first thickness of fabric and is therefore invisible; the operator must constantly check the width of the fold, by turning the fabric over or by feeling the edges of the elastic and of the fabric.